What is the integral of x/(1+10x^2) ?

The integral of x/(1+10x^2) is 1/20 ln|1+10x^2|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x/(1+10x^2)

\int \frac{x}{1 + 10 x ^{2}} d x

\frac{1}{20} ln 1 + 10 x^{2} + C

Solution steps

\int \frac{x}{1 + 10 x ^{2}} d x

Apply u-substitution

: \int \frac{1}{20 u} d u

= \int \frac{1}{20 u} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{20} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{20} ln ∣ u ∣

Substitute back

u = 1 + 10 x^{2}

= \frac{1}{20} ln 1 + 10 x^{2}

Add a constant to the solution

= \frac{1}{20} ln 1 + 10 x^{2} + C

\int \frac{1}{( x + 2 ) ^{4}} d x

\int \frac{6}{2 x - 1} d x

\int 4 x^{- \frac{1}{2}} d x

\int \frac{x ^{3}}{3 x - 2} d x

\int \frac{( x ^{5} + x ^{4} - 8 )}{( x ^{3} - x )} d x

What is the integral of x/(1+10x^2) ?
The integral of x/(1+10x^2) is 1/20 ln|1+10x^2|+C